Fighter can't stave off the later rounds in the later levels. 3-5 is where it starts to get hard to advance to the enemy and hit them, or even protect yourself. The game gets harder by a good amount for Fighters, spiders that slow you down to a crawl (Have fun trying to get in range to kill, while everything stacks up...), monsters that shoot a stream of bullets at lightning speed that slow down as they go farther, and monsters that shoot bullets starting from a small distance away-- the distance a fighter would be at. You can't deflect a bullet that spawned on you.
The game bosses get funner and more bullet hell/Touhou-ish as it goes on. One of them shot rapid homing bullets for about 5 seconds (Don't back yourself in a corner...=P ), another shot pure patterns of bullets, and had less delay between attacks giving less opportunity to hit them.
Some bosses also power-up once their health hit halfway, a yellow spiky ring emits from them and their bullets go faster and could be different, boss may change forms, and they move faster themselves. Lasts about a minute though. Pretty sure they can just reactivate it again.